Park at Alpental, near the Snow Lake Trailhead.
Start up the Cave Ridge / Snoqualmie Peak "trail" that starts 100ft or so south of the Snow Lake Trail. Once you get to a large clearing (maybe about 4000' - 4200' elevation?) you leave the route that goes up to Snoqualmie Peak and start climbing up to the right. I believe there is a trail in summer; in winter, you may not have many clues as most or all footprints will continue towards Snoqualmie. From here climb up to the saddle between Cave Ridge and Guye Peak. Make a right and roughly follow the ridge to Guye's north peak.
From the north peak, you have two options to reach the notch below you to the south. The standard route follows a steep gully to the left (east) 60 feet below the summit. Descend this gully some 70 feet until you reach the next gully, and follow this up to the notch between the north and middle peaks. This route is very steep but apparently only class 3 in the summer. There are rappel rings in the notch between the north and middle peaks, indicating enough people found it steep enough to use a rope. In the winter/spring, snow fills these gullies and they become somewhat intimidating. Under these conditions, consider using a rope and a couple pickets and using trees at the tops of the gullies.
The second option I call the "Hidden Ridge" route and have not found documented. It consists of rappelling a short (30-40ft) pitch of rock, leaving the rope, and top-roping back up on the return. As you stand on the north summit looking south, you will see an outcropping just below you on the ridge. Following this ridge and hidden behind the outcropping is the "Hidden Ridge". 10-15 feet below the N summit traverse around the summit to the right (west) for about 100 ft to reach the outcropping. From here you can sling a horn (I recommend the more stable one further from the edge) and rap down about 30 ft to the notch between the N and middle summits. (The rock here was snow-free in January 2014). Leave the rope here and continue. On the way back, you can top-rope this section. Is is straight-forward class 4/low class 5, having just one move about 5.4.
From the notch to the south peak is straight-forward. From the middle peak you can follow a short gully to the east, or scramble down a steep but blocky class 3 face (recommended and easier than it looks from the top), and walk on to the south peak (Guye's true summit)!
In mid-to-late summer after the snow has melted: none.
In winter/spring: ice axe, 30m light/glacier rope. For the standard gullies route add to this: webbing to sling trees and maybe a couple pickets. For the "Hidden Ridge" variation: a long piece of webbing to sling the horn, and slings to extend to the pitch edge (cordalette + a couple double slings work)